Let \(\le \)  be the center of \(\) , the group \(/\)  is semisimple and so the image of \(\)  under the central quotient map is a normal subgroup of a semisimple group so is semisimple (see [1]}). Thus \(Z(N/Z)\)  is compact, hence by compactness of \(Z\) , \(Z(N)\)  is compact.
